The present invention relates to a radial-flow wheel for a turbo-engine having a hub and blades distributed on the hub-side outer circumference.
The significant disadvantage of a radial-flow compressor is the fact that it achieves only an isentropic stage working efficiency of approximately 80 to 84%. In addition to the increasing and detaching of the boundary layer in the housing area this is the result of the fact that the frictional losses between the fluid and the radial-flow wheel and the following diffuser are significantly higher than in the case of an axial-flow compressor.
In this context, the term radial-flow wheel includes an impeller in the case of which the flow direction at the outlet is not strictly radial but also has an axial component.
A disadvantage of conventional radial-flow wheels is the fact that the surfaces of the wheel against which the fluid flows are relatively large, whereby the friction-caused flow losses are increased.
In addition, it is known in the case of radial-flow wheels, to displace the leading edge of some of the blades a certain distance toward the rear in order to reduce the partial blocking of the flow duct caused by the blades and thus ensure the required mass flow. A reduction of the friction-caused flow losses cannot be achieved in this manner.
Based on the above, it is an object of the present invention to develop a radial-flow wheel in such a manner that the frictionally caused flow losses are reduced in comparison to conventional radial-flow wheels.
For a radial-flow wheel of the above-mentioned type, this object is achieved according to a first embodiment of the invention by the fact that the meridian section contour of the outer surface of the hub is a catenarian curve.
In especially preferred embodiments, the catenarian curve can be represented in the form of an axial course (z) as a function of the radius (r) by z=f(r), in which case the contour is by approximation determined by the following solution of the differential equation for minimal surfaces, EQU z=d+c arch (r/c)
wherein c and d are constants which result from the edge conditions at the inlet and outlet of the radial-flow wheel, and wherein arch (r/c) is the arcus cosinus hyperbolicus of r/c. The differential equation for minimal surfaces is known from Dr. Bernhard Baule's, "Die Mathematik des Naturforschers und Ingenieurs", Part 2, Publishers Harri Deutsch, Frankfurt/Main, Par. 11, Page 46, 1979. The constants c and d are determined by means of two parameters respectively out of four possible parameter which are the angle of flow, the angle of slope, the axial distance or the radius for the edge conditions at the inlet and outlet of the radial-flow wheel.
The principal advantages of this development of the invention are that a radial-flow wheel having such contours of the outer surface of the hub, in comparison to conventional radial-flow wheels, has a reduced surface in this partial area of the flow duct, and thus the frictional losses on the outer surface of the hub are minimized. The surprisingly resulting course of a catenarian curve according to the invention corresponds to the curve which a chain takes up which is hung between two points of different heights.
Preferably, both surfaces, thus the outer surface of the hub and the enveloping surface of the housing-side outer contour of the blades are provided with a catenarian curve as a meridian section contour in order to obtain the smallest possible surface (minimal surface) in the direction of the housing as well as in the direction of the hub. However embodiments are also contemplated wherein only one of the two surfaces--the outer surface of the hub or the enveloping surface--is shaped according to the invention while the other surface has a conventional design.
It is up to the person skilled in the art to provide, within the scope of the invention, a slight deviation from the ideal catenarian curve if, as a result, other fluidic characteristics can be improved and the resulting surface enlargement remains slight.
Naturally, the inlet or outlet area of the outer surface of the hub or of the enveloping surface of the outer contour of the blades of a radial-flow wheel in its contour may also deviate from the ideal catenarian curve in order to meet specific inlet or outlet requirements.
In addition, the developments described above as well as below apply to radial-flow wheels without any shroud as well as to those with a shroud, which means that in the latter case the enveloping surface of the outer contour of the blades is to be replaced by the inner surface of the shroud.
According to a second embodiment of the invention, the object on which the invention is based is achieved in that the blade surfaces or sections of them are constructed as screw surfaces (minimal surfaces) which are a function of the angle at circumference (.psi.) by z=f(.psi.) and of the radius (r), the blade surfaces by approximation being determined by the vector function (r), with the angle at circumference (.psi.) and the radius (r) as scalar variables and with ##EQU1## as well as with x, y, z as the space coordinates and with l and k as the constants which are determined by the edge conditions for, for example, the axial distance z and the angle at circumference .psi. at the inlet and outlet of the radial-flow wheel. Such screw surfaces are solutions of the differential equation for minimal surfaces wherein the equation shows that any radial of the blade surface passes through the centerline of the hub.
The vector function (r) according to the invention in a cartesian coordinate system describes the surfaces formed by the blades in order to achieve a minimizing of the surfaces against which the flow medium flows while maintaining given known contours for the hub-side outer surface or the enveloping surface of the housing-side outer contour of the blades and blade numbers. This development of the blade surfaces as screw surfaces permits a reduction of the flow losses and thus an increase of the efficiency for a radial-flow wheel according to the invention.
In a further development of this solution of the object according to the invention, the blade surfaces may again in partial areas, particularly in the blade inlet or outlet area, deviate from this contour with a minimal surface without leaving the scope of the invention.
Preferably, the blades have an approximate screw surface as their surface from the inlet to at least half the length of the filament of flow, i.e. the flow path, of the radial-flow wheel. Such a construction of the blade surfaces of the radial-flow wheel advantageously utilizes the idea of the invention for improving the efficiency.
Another preferred embodiment of the invention provides that the surfaces of the blades, on the outlet side, have approximate screw surfaces which extend along at least half the length of the filament of flow of the radial-flow wheel. By means of this development, the efficiency can be advantageously improved in comparison to the conventional blade development of a radial-flow wheel.
Another advantageous development of the invention provides that the spatial curves of the cutting line, i.e. the line of intersection between two surfaces, of the blade surface and the outer surface of the hub and/or the cutting line of the blade surface and the housing-side outer contour of the blades is a chain-screw curve, i.e. the result of a helical curve when viewed in a front view and a catenarian curve when viewed in a meridian section view. The chain-screw curve is a vector function (r) with the angle at circumference (.psi.) as the scalar variable and with ##EQU2## wherein c, d, l and k are constants which are determined from the edge conditions at the inlet and outlet of the radial-flow wheel. These constants are the same as described above.
This construction combines the advantages of the two above-described embodiments such that a minimizing of the hub-side and housing-side surfaces can be achieved and that, at the same time, the blade surfaces have minimized surfaces. In the case of this construction, on the whole, a higher reduction of the friction losses can be achieved than in the case of the minimal surface construction of the hub-side outer surface or the enveloping surface of the housing-side outer contours of the blades or the blade surface.
In this context, a chain-screw line is a spatial curve which with the angle as the independent parameter depends only on the angle (.psi.) itself. It is the result of a helical curve in the front view and a catenarian curve in the meridian section.
According to another embodiment of the invention, in the case of a radial-flow wheel for a turbo-engine according to the invention, the number of blades is changeable in the axial direction, the blades being arranged behind one another in the flow direction, and in each meridian normal section along the flow duct at an angle of slope (.epsilon.) with respect to the radial direction with a hub radius (R.sub.N) and a housing radius (R.sub.G), the number (n) of blades in the flow direction by approximation being determined by the following equation for n: ##EQU3##
The construction according to the invention has the advantage that, for a given flow duct cross-section (A) which is bounded by two blades, a hub-side and a housing-side enveloping surface of the blades, a minimal circumference (U) is achieved. By means of a step-by-step increase of the blade number in the flow direction in the case of compressor impellers, or a step-by-step decrease of the blade number in the flow direction in the case of turbine wheels according to the above equation, the surfaces in the flow duct against which the flow occurs are reduced, decreasing the frictionally caused flow losses.
Preferably, the number of blades is doubled step-by-step in specific axial points. In particular, two axial points are provided at which the number of blades doubles PG,9 in each case. That means that the leading edges of an equal number of shorter blades, which are spaced between the blades starting at the inlet, are disposed at a first axial position. This also occurs at a second axial position s that in the area of the radial-flow wheel outlet of a compressor impeller or of the radial-flow wheel inlet of a turbine wheel, four times the number of blades exist than at the inlet of a compressor impeller or at the outlet of a turbine wheel. When the blade number is doubled at three axial points, the blade number at the outlet is eight times higher than at the inlet.
The determination of those axial points at which the leading edges of the blades displaced toward the rear are located, will be made by the person skilled in the art in coordination with other required flow characteristics. In particular, the axial point may be provided in that position in which the optimal blade number according to the above-mentioned formula has reached twice the value of the blades which were actually present up to that time. However, it is expedient to displace the axial point farther toward the front in order to achieve a loss of efficiency that is as low as possible.
It is advantageous for at least two successive axial sections to be provided with blades which are distributed on the circumference and extend only along the axial length of a section, the trailing edges of the preceding group of blades being followed by the leading edges of the next group of blades in a manner that is staggered in the circumferential direction. The groups of blades may also slightly overlap axially. In particular, three or four successive sections are provided. This construction has the significant advantage that, instead of a doubling of the blade number, arbitrary blade number increases are possible. For example, the blade number in four sections may gradually be increased from 9 to 13 to 23 and finally to 56. In this case, the blades are normally constructed to be only as long as the course of the corresponding axial section; that is, no or only very few blades are provided which extend along the whole radial-flow wheel length. The sections preferably have the same length. However, if necessary, the sections may extend in different manners. This further development of the idea of the invention permits a best possible adaptation of the blade number, which necessarily changes in discrete steps, to the blade number n, which is optimal with respect to the surface minimizing, according to the above-mentioned equation for n.
Preferably, the blades are manufactured in such a manner that they have minimal surfaces; that is, that the blade surfaces, or at least significant parts of the blade surfaces, are constructed as screw surfaces. In addition, it is particularly advantageous for the hub-side outer surface and/or the housing-side rotation surface at the same time to be shaped in such a manner that they have a contour of the type of a catenarian curve in a meridian section. A radial-flow wheel of this type is optimized from the point of view of the frictional resistance; that is, it has the smallest possible surface.
According to an advantageous further development of the invention, the exposed blade edges, along a part of the course or along the whole course, experience a circumferential curvature which is equal to are more pronounced than the meridian curvature. This construction reduces the danger of burblings in the area of the blade tips which also reduce the efficiency.
Preferably, the blades have a backward curvature. A backward curvature means, on the one hand, that the rotating direction of the impeller is opposite to the rotating direction of a particle flowing through the impeller and, on the other hand, that at the impeller outlet, the circumferential component of the mean relative speed vector has the opposite direction of the circumferential speed. The backward curvature has the advantage that, in addition, aerodynamic stress is reduced.
Other objects, advantages and novel features of the present invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.